K-type and H-type transitions of natural convection boundary layers

Significance 

Transition from laminar to turbulent flow has been a puzzle in fluid mechanics owing to the importance of the behavior of this transition. Previously, it had been understood that aerodynamics, heat transfer, and mass transport features vary considerably in turbulent and laminar flow regimes. Recently, researchers focused on several experimental, numerical and, theoretical research on flow transitions in Blasius boundary layers. Unfortunately, hardly any research was conducted concerning transitions in natural convection boundary layers.

K-type and H-type transitions are the typical transitions observed in Blasius boundary layers. It is important to investigate if H- and K- type transitions observed in Blasius boundary layers occur in natural convection boundary layers, although the velocity regime of the natural convection boundary layer is different from the velocity regime of the Blasius boundary layer.

The issues of laminar-turbulent transition in the Blasius boundary layers has received more research attention for more than half a century. It has been observed that natural transition to turbulence follows three main stages. The first stage is marked by stream-wise amplification of the unstable 2-dimensional Tollmien-Schlitching waves. As the waves moves downstream, three dimensionality occurs and the flow becomes fully 3-dimensional, which is marked by the development of 3-dimensional vertical structures. This is the second stage. Flowing further downstream the flow becomes turbulent, and is described by the development of turbulent spots and intermittent phenomena.

University of Sydney researchers, Dr. Yongling Zhao, Professor Chengwang Lei and Professor John Patterson investigated the K- and H-type transitions of a natural convection boundary layer of a fluid of Prandtl number 7 by the means of 3-dimensional direct numerical simulation. These transition were the various flow features at the transitional stage from laminar to turbulence initiated by two forms of perturbations. Their research work is published in Journal of Fluid Mechanics.

The authors introduced superimposed Tollmien-Schlichting and oblique waves of identical frequency in the boundary layer in order to excite the K-type transition. However, for the case of H-type transition, they introduced superimposed Tollmien-Schlichting and oblique waves of different frequencies. The frequency of the oblique waves was half the frequency of the Tollmien-Schlichting waves.

The authors observed that a three-layer longitudinal vortex structure appeared in the boundary layer undergoing the K-type transition. They observed for the first time the typical aligned ∧-shaped vortices characterizing the K-type transition in pure natural convection boundary layers. As opposed to the three-layer longitudinal vortex structure in the case of the K-type transition, the authors observed a double-layer longitudinal vortex structure in the boundary layer undergoing H-type transition.

A staggered pattern of the ∧-shaped vortices characterizing the H-type transition was also observed in the downstream boundary layer. The pattern was considered to be initiated by temporal modulation of the Tollmien-Schlichting and the oblique waves. The flow structures observed for the K- and H- type transitions in natural convection boundary layer were qualitatively identical to those identified for the Blasius boundary layers. However, by analyzing the turbulence energy production, the authors observed that the turbulence energy production was by buoyancy rather than Reynolds stresses.

Reference

Yongling Zhao, Chengwang Lei and John C. Patterson. The K-type and H-type transitions of natural convection boundary layers. Journal of Fluid Mechanics (2017), volume 824, page 352–387.

 

Go To Journal of Fluid Mechanics

Check Also

Thermal conductivity of hybrid organic-inorganic crystals and superlattices. Advances in Engineering

Thermal conductivity of hybrid organic-inorganic crystals and superlattices